Individuals often face complex choices where value is not easily realized and the goal is to select the optimal rewards. Deficits in reward processing, or deliberation, are characteristic of many psychiatric diseases. For example, schizophrenia patients appear unable to represent the value of all available choice options, and therefore fail to select actions that have the highest values. Contemporary treatment options for many psychiatric diseases, including schizophrenia, target dopamine. Dopamine neurons code subjective value. However, dopamine responses do not display extended physiological profiles of neurons involved in deliberation. Thus, the neurocomputational mechanisms of deliberation likely involve reward structures to which dopamine neurons project. The goals of this research are to formalize the investigation of value deliberation using mathematical optimization theory, and to uncover the neuronal algorithms and implementation of optimization over value. With these aims in mind, monkeys will be trained in a behavioral paradigm based on a combinatorial optimization problem, the knapsack problem (KP). Given a number of objects with different values and weights, the KP asks what is the most valuable subset of the objects that a knapsack can carry without breaking. Despite this apparent simplicity, the fastest computers cannot find and verify the optimal solution to the KP because the computational complexity scales directly with the number of objects. We will use computational complexity to modulate the difficulty of the behavioral task. Monkeys will select a set of rewards that fit inside a virtual knapsack. Choose too few, and they will harvest less reward than optimal. Exceed the capacity of the knapsack, and it will `break' and not deliver reward. We will use operations research algorithms to estimate the heuristics used to optimize over rewards. We will record from the striatum and prefrontal cortex. Both structures are dopamine projection targets, and both are implicated in psychiatric and neurodegenerative diseases. I will use optogenetics and electrophysiology to investigate direct and indirect pathway striatal neurons. These two neuron populations have distinct projection fields and opposing effects on thalamic output. Likewise the dopamine value signal has opposing influences on direct and indirect pathway neurons, and this points to differential role for direct and indirect pathway neurons in value-based deliberation. Thus, I will investigate how value-based deliberation is differentially reflected in these pathways. The prefrontal cortex mediates value comparison, and dopamine release is hypothesized to mediate those value comparisons. I will use optogenetics and electrophysiology to investigate prefrontal excitatory and inhibitory neurons and their respective roles during value-based deliberation. The findings will reveal the neural algorithms used to optimize value, reveal the neuron-type specific implementation of those algorithms, provide mechanistic insights regarding psychiatric diseases, and develop a foundation for circuit therapies to correct reward processing deficits.